When the polynomial P(x) = 5x3 − 51x2 + kx − 9 is divided by x − 9, the remainder is 0. Which of the following is also a factor of P(x)?

Question

anonymous · Answer

A. x − 5
B. x + 1
C. x − 1
D. 5x + 1

campbell_st · Answer

well the easy solution is to use the factor theorem and ingore any polynomial of synthetic division 

so the 1st task is to find the value of k... 

so if x - 9 is a factor then x = 9 is a zero 

so substitute x = 9 into the polynomial to find the value of k... 

so 

$$0 = 5(9)^3 -51(9)^2 + 9k -9$$ 

then when you get k... look at the other factors... 

the constant term is -9  so if (x - 9) is a factor... then (x -5) can't be... it would give a constant term that is at least 45

so look at 

x + 1   if its a factor then x = -1 is a possible zero

same for x -1  is its a factor x = 1 is a possible zero... 

and the repeat it for 5x + 1   then x = 1/5 is a possible zero

anonymous · Answer

can you help with another question please

campbell_st · Answer

just post the question as a new question and lots of people can help